The Maxwell-Dirac equations are the equations for electronic matter, the “classical” theory underlying QED. The system combines the Dirac equations with the Maxwell equations sourced by the Dirac current. A stationary Maxwell-Dirac system has ψ = eφ, with φ independent of t. The system is said to be isolated if the independent variables obey quite weak regularity and decay conditions. In this p...

Dirac semimetals have attracted extensive attentions in recent years. It has been theoretically suggested that many-body interactions may drive exotic phase transitions, spontaneously generating a Dirac mass for the nominally massless Dirac electrons. So far, signature of interaction-driven transition has been lacking. In this work, we report high-magnetic-field transport measurements of the Di...

A Dirac fermion in a topological Dirac semimetal is a quadruple-degenerate quasiparticle state with a relativistic linear dispersion. Breaking either time-reversal or inversion symmetry turns this system into a Weyl semimetal that hosts double-degenerate Weyl fermion states with opposite chiralities. These two kinds of quasiparticles, although described by a relativistic Dirac equation, do not ...

Graphene, the first discovered 2D Dirac material, has had a profound impact on science and technology. In the last decade, we have witnessed huge advances in graphene related fundamental and applied research. Here, based on first-principles calculations, we propose a new 2D Dirac band on the Si(111) surface with 1/3 monolayer halogen coverage. The sp(3) dangling bonds form a honeycomb superstru...

For any n-dimensional compact spin Riemannian manifold M with a given spin structure and a spinor bundle ΣM , and any compact Riemannian manifold N , we show an ǫ-regularity theorem for weakly Dirac-harmonic maps (φ, ψ) : M ⊗ΣM → N ⊗ φ∗TN . As a consequence, any weakly Dirac-harmonic map is proven to be smooth when n = 2. A weak convergence theorem for approximate Dirac-harmonic maps is establi...

In a companion paper, we introduced a notion of multi-Dirac structures, a graded version of Dirac structures, and we discussed their relevance for classical field theories. In the current paper we focus on the geometry of multi-Dirac structures. After recalling the basic definitions, we introduce a gradedmultiplication and amulti-Courant bracket on the space of sections of a multi-Dirac structu...

Two-dimensional (2D) materials are well-known to exhibit interesting phenomena due to quantum confinement. Here, we show that quantum confinement, together with structural anisotropy, result in an electric-field-tunable Dirac cone in 2D black phosphorus. Using density functional theory calculations, we find that an electric field, E ext, applied normal to a 2D black phosphorus thin film, can re...

The spectral flow of the hermitian Dirac–Wilson operator H(m) has been used to construct a lattice version of the index of the Dirac operator. We clarify some aspects of this construction by showing the following (in 4D): When the curvature of the lattice gauge field satisfies an approximate smoothness condition, crossings of the origin by eigenvalues of H(m) can only happen when m is close to ...

In 1951, Gabriel Dirac conjectured that every set P of n non-collinear points in the plane contains a point in at least n 2 − c lines determined by P , for some constant c. The following weakening was proved by Beck and Szemerédi–Trotter: every set P of n non-collinear points contains a point in at least n c lines determined by P , for some large unspecified constant c. We prove that every set ...

We recently performed a pilot study determining the parameters of the leading order chiral La-grangian from distributions of the eigenvalues of a quenched Dirac operator coupled to an imaginary isospin chemical potential. We complement a quick survey of our recent preprint [1] by addressing some points raised during discussions at the conference.